In wireless communications, doubly-selective channels are subject to a time-varying multi-path fading, which leads to both inter-carrier interference (ICI) and inter-symbol interference (ISI) when multi-carrier transmission schemes are employed. This is a particular problem in a wideband wireless network with mobile transceivers, e.g. in vehicular communications networks and millimeter-wave cellular networks where the velocities of the communicating entities can be large and will cause rapid variation in the wireless channel. Adaptive equalization and pilot symbols are normally used to compensate for these fading effects. However, the pilot symbols reduce the spectrum efficiency and data transmission rate given finite radio frequency resources. Moreover, the pilot symbols are only effective for slow fading channels. Channel estimation to obtain channel state information (CSI) is considerably more difficult in doubly-selective fading channels due to the presence of both ISI and ICI.
Several transmission data formats, including differential modulations, can be used for non-coherent communications, which do not rely on any pilots. Such modulation formats work well either for time-selective slow fading or for frequency-selective fading channels. However, for highly-selective fading in both time and frequency domains (i.e., doubly-selective fading), conventional non-coherent transmission schemes degrade significantly.
A basis expansion model (BEM) has been used to approximate singly-selective fading channels. The BEM is used for an iterative semi-blind equalizer based on an expectation-and-maximization (EM) procedure. With help of error correcting codes (ECC), BEM can realize quasi non-coherent communications with a relatively small number of pilot symbols. However, this technique still relies on pilot symbols and ECC soft-decision feedbacks, and no techniques are known that work in purely non-coherent communications over doubly-selective fading channels without any pilot symbols at all.
Another important technique in wireless communications is spatial, temporal, and frequency diversity techniques that reduce a probability that the channel fades deeply on all diversity branches simultaneously. It has been verified that multiple-input multiple-output (MIMO) techniques, which use multiple transmit and receive antennas for spatial diversity or multiplexing, can significantly improve the communications reliability or the channel capacity. For advanced radio communications, most transceivers are often equipped with multiple antennas to achieve the MIMO gain.
For non-coherent communications over MIMO flat-fading channels, it has been theoretically shown that an orthogonal space-time block code (STBC) over a Grassmannian manifold can achieve the channel capacity. However, STBC does not perform well for non-coherent MIMO doubly-selective fading channels due to the strong ISI and ICI. Because the ISI and ICI cause a severe error floor, the maximum spectrum efficiency is seriously restricted.